Abstract: The high-pressure pump has at least one pump element which has a pump plunger which is driven in a reciprocating motion and defines a pump working space into which fuel is drawn in from a fuel feed via an inlet valve during the suction stroke of the pump plunger and from which fuel is displaced into a high-pressure region via an outlet valve during the delivery stroke of the pump plunger. The inlet valve and/or the outlet valve has a valve member at least approximately in the shape of a ball which acts as a sealing surface with a valve seat arranged in a valve housing. The valve member, in its open state, is lifted with its sealing surface from the valve seat, a first cross section of flow is cleared between the valve member and the valve seat, and downstream of the first cross section of flow, a second cross section of flow is formed between the valve member and the valve housing.